Mix the dough by combining flour and salt. Beat the eggs with olive oil and water. Gradually pour the egg mixture into the flour, kneading until you get a elastic and smooth dough. Cover the finished dough with a cloth and let it rest for 30 minutes.
Dice the eringi mushrooms finely and sauté them with shallots in heavy cream.
Roll out the thin dough, then cut it into squares using a ravioli cutter or a square stamp for ravioli. Stuff the dough with the mushroom filling and seal all the edges.
Cook in boiling salted water for 4 minutes. Serve with grated Parmesan and sautéed eringi mushrooms if desired.